Rate of Convergence for sin(1/x^2) with Maclaurin is undefined?

I decided to put my attempt at a solution before the question, because the "solution" is what my question is about.

1. The problem statement, all variables and given/known data
Find the rate of convergence for the following as n->infinity:
lim [sin(1/n^2)]
n->inf

Let f(n) = sin(1/n^2) for simplicity.

2. The attempt at a solution
I was searching through other forums and resources, and finally found a solution.
It said to use the Maclaurin Series (thus x0 = 0), but this would make every term
to look like:

3. Relevant equations
How can we solve when 1/0 is undefined?
For example, in *every* term we have a sin(1/0^x) somewhere. This doesn't work, obviously.

This is solvable using the first few terms of the Maclaurin polynomial according to other sources, but I do not understand how. Did I overlook something? Or am I fundamentally misunderstanding the question?